Help Im bad at geometry
In triangle ABC, let the angle bisectors be BY and CZ. Given AB = 16, AY = 16, and CY = 16, find BC and BZ.
Let's denote the lengths of BC and BZ as x and y, respectively.
According to the angle bisector theorem, we have:
AY / CY = AB / BC
Substituting the given values, we get:
16 / 16 = 16 / x
Cross-multiplying, we have:
16x = 16 * 16 16x = 256 x = 256 / 16 x = 16
So, BC = 16.
Now, let's consider triangle BCZ. Using the angle bisector theorem again, we have:
BZ / CZ = BC / CY
Substituting the known values, we get:
y / 16 = 16 / 16
Simplifying, we have:
y / 16 = 1
Cross-multiplying, we get:
y = 16
Therefore, BC = 16 and BZ = 16.